The purpose of this thesis is to demonstrate that two-girder or two-web structural systems can be employed to design efficient bridges with an adequate level of redundancy. The issue of redundancy in two-girder bridges is a constraint for the bridge designers in North America who want to take advantage of efficiency in this type of structural system. Therefore, behavior of two-girder or two-web structural systems after failure of one main load-carrying component is evaluated to validate their safety. A procedure is developed to perform system-level reliability analysis of bridges. This procedure is applied to two bridge concepts, a twin steel girder with composite deck slab and a concrete double-T girder with unbonded external tendons. The results show that twin steel girder bridges can be designed to fulfill the requirements of a redundant structure and the double-T girder with external unbonded tendons can be employed to develop a robust structural system.

The purpose of this thesis is to demonstrate that two-girder or two-web structural systems can be employed to design efficient bridges with an adequate level of redundancy. The issue of redundancy in two-girder bridges is a constraint for the bridge designers in North America who want to take advantage of efficiency in this type of structural system. Therefore, behavior of two-girder or two-web structural systems after failure of one main load-carrying component is evaluated to validate their safety. A procedure is developed to perform system-level reliability analysis of bridges. This procedure is applied to two bridge concepts, a twin steel girder with composite deck slab and a concrete double-T girder with unbonded external tendons. The results show that twin steel girder bridges can be designed to fulfill the requirements of a redundant structure and the double-T girder with external unbonded tendons can be employed to develop a robust structural system.

Simultaneous stabilization is an important problem in the design of robust controllers. It is the problem of designing a single feedback controller which will simultaneously stabilize every member of a finite collection of liner time-invariant systems. This provides simplicity and reliability which is desirable in aerospace applications. It can be used as a back-up control system in sophisticated airplanes, or an inexpensive primary one for small aircraft. In this work the robustness of the simultaneous stabilization problem, known as the Robust Simultaneous Stabilization (RSS) problem, is addressed. First, an optimization methodology for finding a solution to the Simultaneous Stabilization (SS) problem is proposed. Next, in order to provide simultaneous stability while maximizing the stability robustness bounds, a multiple-robustness optimization design methodology for the RSS problem is presented. The two proposed design methodologies are then compared in terms of robustness of the designed controller.

The purpose of this thesis was to design controllers by using H1 and &sup1 / control strategies in order to suppress the free and forced vibrations of smart structures. The smart structures analyzed in this study were the smart beam and the smart &macr / n. They were aluminum passive structures with surface bonded PZT (Lead-Zirconate-Titanate) patches. The structures were considered in clamped-free con&macr / guration. The &macr / rst part of this study focused on the identi&macr / cation of nominal system models of the smart structures from the experimental data. For the experimentally identi&macr / ed models the robust controllers were designed by using H1 and &sup1 / -synthesis strategies. In the second part, the controller implementation was carried out for the suppression of free and forced vibrations of the smart structures. Within the framework of this study, a Smart Structures Laboratory was established in the Aerospace Engineering Department of METU. The controller implementations were carried out by considering two di&reg / erent experimental set-ups. In the &macr / rst set-up the controller designs were based on the strain measurements. In the second approach, the displacement measurements, which were acquired through laser displacement sensor, were considered in the controller design. The &macr / rst two &deg / exural modes of the smart beam were successfully controlled by using H1 method. The vibrations of the &macr / rst two &deg / exural and &macr / rst torsional modes of the smart &macr / n were suppressed through the &sup1 / -synthesis. Satisfactory attenuation levels were achieved for both strain measurement and displacement measurement applications.

One-way and two-way classification models in experimental design for both balanced and unbalanced cases are considered when the errors have Generalized Secant Hyperbolic distribution. Efficient and robust estimators for main and interaction effects are obtained by using the modified maximum likelihood estimation (MML) technique. The test statistics analogous to the normal-theory F statistics are defined to test main and interaction effects and a test statistic for testing linear contrasts is defined. It is shown that test statistics based on MML estimators are efficient and robust. The methodogy obtained is also generalized to situations where the error distributions from block to block are non-identical.

Naive Bayes classifier and maximum likelihood hypotheses in Bayesian learning are considered when the errors have non-normal distribution. For location and scale parameters, efficient and robust estimators that are obtained by using the modified maximum likelihood estimation (MML) technique are used. In naive Bayes classifier, the error distributions from class to class and from feature to feature are assumed to be non-identical and Generalized Secant Hyperbolic (GSH) and Generalized Logistic (GL) distribution families have been used instead of normal distribution. It is shown that the non-normal naive Bayes classifier obtained in this way classifies the data more accurately than the one based on the normality assumption. Furthermore, the maximum likelihood (ML) hypotheses are obtained under the assumption of non-normality, which also produce better results compared to the conventional ML approach.

In our study, the superhydrophobic surface based on biomimetic lotus leave is explored to maintain the desired properties for self-cleaning. In controlling bead-up and roll-off characteristics of water droplets the contact angle and contact angle hysteresis were very important and we investigated the determining conditions on different model surfaces with micro- and nanostructures. Two governing equations were proposed, one for contact angle based on Laplace pressure and one for contact angle hysteresis based on Young-Dupré equation. Based on these understanding on superhydrophobicity, possible applications of the superhydrophobicity for self-cleaning and water repellency were explored and application related technical issues were addressed. Based on our understanding of the roughness effect on superhydrophobicity (both contact angle and hysteresis), structured surfaces from polybutadiene, polyurethane, silica, and Si etc were successfully prepared. For engineering applications of superhydrophobic surfaces, stability issues regarding UV, mechanical robustness and humid environment need to be investigated. Among these factors, UV stability is the first one to be studied. Silica surfaces with excellent UV stability were prepared. UV stability on the surface currently is 5,500 h according the standard test method of ASTM D 4329. No degradation on surface superhydrophobicity was observed. New methods for preparing superhydrophobic and transparent silica surfaces were investigated using urea-choline chloride eutectic liquid to generate fine roughness and reduce the cost for preparation of surface structures. Another possible application for self-cleaning in photovoltaic panels was investigated on Si surfaces by construction of the two-scale rough structures followed by fluoroalkyl silane treatment. Regarding the mechanical robustness, epoxy-silica superhydrophobic surfaces were prepared by O2 plasma etching to generate enough surface roughness of silica spheres followed by fluoroalkyl silane treatment. A robustness test method was proposed and the test results showed that the surface is among the most robust surfaces for the superhydrophobic surfaces we prepared and currently reported in literature.

We study the consistency, robustness and efficiency of parameter estimation in different but related models via semiparametric approach. First, we revisit the second- order least squares estimator proposed in Wang and Leblanc (2008) and show that the estimator reaches the semiparametric efficiency. We further extend the method to the heteroscedastic error models and propose a semiparametric efficient estimator in this more general setting. Second, we study a class of semiparametric skewed distributions arising when the sample selection process causes sampling bias for the observations. We begin by assuming the anti-symmetric property to the skewing function. Taking into account the symmetric nature of the population distribution, we propose consistent estimators for the center of the symmetric population. These estimators are robust to model misspecification and reach the minimum possible estimation variance. Next, we extend the model to permit a more flexible skewing structure. Without assuming a particular form of the skewing function, we propose both consistent and efficient estimators for the center of the symmetric population using a semiparametric method. We also analyze the asymptotic properties and derive the corresponding inference procedures. Numerical results are provided to support the results and illustrate the finite sample performance of the proposed estimators.

La classe des M-estimateurs engendre des estimateurs classiques d’un paramètre de localisation multidimensionnel tels que l’estimateur du maximum de vraisemblance, la moyenne empirique et la médiane spatiale. Huber (1964) introduit les M-estimateurs dans le cadre de l’étude des estimateurs robustes. Parmi la littérature dédiée à ces estimateurs, on trouve en particulier les ouvrages de Huber (1981) et de Hampel et al. (1986) sur le comportement asymptotique et la robustesse via le point de rupture et la fonction d’influence (voir Ruiz-Gazen (2012) pour une synthèse sur ces notions). Plus récemment, des résultats sur la convergence et la normalité asymptotique sont établis par Van der Vaart (2000) dans le cadre multidimensionnel. Nevalainen et al. (2006, 2007) étudient le cas particulier de la médiane spatiale pondérée et non-pondérée dans le cas clusterisé. Nous généralisons ces résultats aux M-estimateurs pondérés. Nous étudions leur convergence presque sûre, leur normalité asymptotique ainsi que leur robustesse dans le cas de données clusterisées. / M-estimators were first introduced by Huber (1964) as robust estimators of location and gave rise to a substantial literature. For results on their asymptotic behavior and robustness (using the study of the influence func- tion and the breakdown point), we may refer in particular to the books of Huber (1981) and Hampel et al. (1986). For more recent references, we may cite the work of Ruiz-Gazen (2012) with a nice introductory presentation of robust statistics, and the book of Van der Vaart (2000) for results, in the independent and identically distributed setting, concerning convergence and asymptotic normality in the multivariate setting considered throughout this paper. Most of references address the case where the data are independent and identically distributed. However clustered, and hierarchical, data frequently arise in applications. Typically the facility location problem is an important research topic in spatial data analysis for the geographic location of some economic activity. In this field, recent studies perform spatial modelling with clustered data (see e.g. Liao and Guo, 2008; Javadi and Shahrabi, 2014, and references therein). Concerning robust estimation, Nevalainen et al. (2006) study the spatial median for the multivariate one-sample location problem with clustered data. They show that the intra-cluster correlation has an impact on the asymptotic covariance matrix. The weighted spatial median, introduced in their pioneer paper of 2007, has a superior efficiency with respect to its unweighted version, especially when clusters’ sizes are heterogenous or in the presence of strong intra-cluster correlation. The class of weighted M-estimators (introduced in El Asri, 2013) may be viewed as a generalization of this work to a broad class of estimators: weights are assigned to the objective function that defines M-estimators. The aim is, for example, to adapt M-estimators to the clustered structures, to the size of clusters, or to clusters including extremal values, in order to increase their efficiency or robustness. In this thesis, we study the almost sure convergence of unweighted and weighted M-estimators and establish their asymptotic normality. Then, we provide consistent estimators of the asymptotic variance and derived, numerically, optimal weights that improve the relative efficiency to their unweighted versions. Finally, from a weight-based formulation of the breakdown point, we illustrate how these optimal weights lead to an altered breakdown point.

An efficient robustness analysis for the VEGA launch vehicle is essential to minimize the potential system failure during the ascending phase. Monte Carlo sampling method is usually considered as a reliable strategy in industry if the sampling size is large enough. However, due to a large number of uncertainties and a long response time for a single simulation, exploring the entire uncertainties sufficiently through Monte Carlo sampling method is impractical for VEGA launch vehicle. In order to make the robustness analysis more efficient when the number of simulation is limited, the quasi-Monte Carlo(Sobol, Faure, Halton sequence) and heuristic algorithm(Differential Evolution) are proposed. Nevertheless, the reasonable number of samples for simulation is still much smaller than the minimal number of samples for sufficient exploration. To further improve the efficiency of robustness analysis, the redundant uncertainties are sorted out by sensitivity analysis. Only the dominant uncertainties are remained in the robustness analysis. As all samples for simulation are discrete, many uncertainty spaces are not explored with respect to its objective function by sampling or optimization methods. To study these latent information, the meta-model trained by Gaussian Process is introduced. Based on the meta-model, the expected maximum objective value and expected sensitivity of each uncertainties can be analyzed for robustness analysis with much higher efficiency but without loss much accuracy.